Uncertainty principles for Jacobi expansions ✩

In this paper an uncertainty principle for Jacobi expansions is derived, as a generalization of that for ultraspherical expansions by Rösler and Voit. Indeed a stronger inequality is proved, which is new even for Fourier cosine or ultraspherical expansions. A complex base of exponential type on the torus {z ∈ C: |z| = 1} related to Jacobi polynomials is introduced, which are the eigenfunctions both of certain differential–difference operators of the first order and the second order. An uncertainty principle related to such exponential base is also proved.  2003 Elsevier Inc. All rights reserved.